Conventionally, a structure for mounting a rear fork on a vehicle such as a motorcycle is known as disclosed for example, in Japanese Patent Laid-Open No. 2000-85673 in which between left and right pivot supporting holes of a body frame, pivot supporting holes of an engine supported by the body frame are arranged so as to become coaxial. In addition, between the pivot supporting holes of the body frame and pivot supporting holes of the engine, there are arranged supporting holes capable of being rotated with respect to left and right arm portions of the rear forks, respectively, so as to become coaxial with those pivot supporting holes; and so as to penetrate those pivot supporting holes of the body frame. The supporting holes are capable of being rotated relative to the rear fork and those pivot supporting holes of the engine, respectively. There is disposed a pivot shaft, whereby the rear fork is rotatively supported. See, Japanese Patent Laid-Open No. 2000-85673(the 4th page, FIG. 4). 
The above-described conventional structure of mounting a rear fork in a vehicle such as a motorcycle has the following problems.
That is, an end surface portion of a pivot supporting hole of a vehicle frame or an engine for supporting a pivot shaft is confined to an extent that merely chamfering work is performed. When a load such as a road reaction force or a driving force is applied to the pivot shaft through the rear fork from the rear wheel, the pivot shaft is going to deflect in accordance with an amount of the load to be applied. At that time, the pivot shaft comes into line-contact with the end surface of the pivot supporting hole of the vehicle frame or the engine by which it is supported. Also, at this time, a strong shearing force is locally exerted on the pivot shaft As a result, the rotational characteristic of the rear fork does not draw any smooth curved line, resulting in a phenomenon in which driving information of the rear wheel becomes difficult to be smoothly conveyed to the driver.